Look at this table: x y 1–2 2–4 3–8 4–16 5–32 Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data. y=

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Look at this table:  x y  1–2  2–4  3–8  4–16  5–32  Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data. y=

Willie · Accepted Answer

The x-values are increasing by 1 each time and the y-values are doubling each time. Since the y-values are increasing by a constant factor of 2, the model must be exponential. The data would have to increase by a constant amount to be linear and the second difference of the y-values would have to be constant for the model to be quadratic.  Notice that each y-coordinate is a power of 2. Since 2=21,4=22,8=23,16=24, and 32=25, then each y-coordinate is a power of 2 where the exponent is the x-coordinate. The equation is then y=2x.

RizerMix · Accepted Answer

Answer:y=−2×(−2)xExplanation:If we observe the y-values closely, we can notice that they are doubling each time the x-value increases by 1. This indicates an exponential relationship, where the y-value is increasing exponentially with respect to the x-value.To find the exponential function that models the data, we can use the general form of an exponential function: y = a(b)^x.To determine the values of &#039;a&#039; and &#039;b&#039;, we can look at the data points given:x:1,2,3,4,5y:−2,4,8,16,32Let&#039;s choose the first data point (x=1, y=-2) to solve for &#039;a&#039; and &#039;b&#039;:−2=a(b)1Solving this equation for &#039;a&#039;, we get:a=−2Now, let&#039;s use the second data point (x=2, y=4) to solve for &#039;b&#039;:4=−2(b)2Solving this equation for &#039;b&#039;, we get:b=−2Substituting the values of &#039;a&#039; and &#039;b&#039; into the exponential function, we have:y=−2×(−2)xTherefore, the exponential function that models the data is:y=−2×(−2)x

Vasquez · Accepted Answer

When we look at the table, we observe that the y-values are increasing at an exponential rate as the x-values increase. Specifically, the y-values are doubling each time the x-values increase by 1. This suggests an exponential relationship.To find the exponential function that models the data, we can use the general form of an exponential function: y=a(b)x.Let&#039;s calculate the values of a and b using the given data:When x = 1, y = 22=a(b)1When x = 2, y = 44=a(b)2Dividing the second equation by the first equation, we get:42=a(b)2a(b)12=bSubstituting the value of b back into the first equation:2=a(2)12=2aSimplifying the equation, we find that a = 1.Therefore, the exponential function that models the data is:y=1(2)xIn conclusion, the function that models the data in the table is:y=2x

Don Sumner · Accepted Answer

Looking at the table, we can see that as x increases by 1, y is multiplied by a certain factor. This suggests an exponential relationship between x and y.To find the exponential function, we need to determine the values of a and b. We can use the first two data points (x=1, y=2) and (x=2, y=4) to find these values.We can rewrite the exponential function in the form of y=a(b)x.Let&#039;s solve it step by step:Step 1: Finding the value of bFrom the first data point, we have:2=a(b)1From the second data point, we have:4=a(b)2Dividing these two equations, we get:4/2=(a(b)2)/(a(b)1)2=bStep 2: Finding the value of aUsing the value of b that we found in Step 1, we can substitute it into one of the original equations. Let&#039;s use the first data point:2=a(2)12=2aa=1Therefore, the exponential function that models the data is:y=1·(2)x

Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data.

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